标题： 沿t-结构的局部化子范畴的分类 显示英文标题

标题： Classification of localizing subcategories along t-structures

摘要： 我们研究稳定$\infty$-范畴$\mathcal{C}$中局部化子范畴与具有$t$-结构$(\mathcal{C}_{\geq 0}, \mathcal{C}_{\leq 0})$的关系，预稳定$\infty$-范畴$\mathcal{C}_{\geq 0}$以及阿贝尔范畴$\mathcal{C}^{\heartsuit}$。 我们证明了$\mathcal{C}^{\heartsuit}$的弱局部化子范畴与$\mathcal{C}$的局部化子范畴之间存在双射关系，其中对象包含性可以在心上进行检查。 这推广了关于诺特环和有界$t$-结构的类似已知对应关系。 我们还证明，这将局部化子范畴的$\mathcal{C}^{\heartsuit}$与局部化子范畴的$\mathcal{C}$之间的双射限制为那些是$t$-正合函子的核，并将 Lurie 在$\mathcal{C}_{\geq 0}$和$\mathcal{C}^{\heartsuit}$之间的局部化子范畴对应关系提升到稳定范畴$\mathcal{C}$。 显示英文摘要

摘要： We study the interplay between localizing subcategories in a stable $\infty$-category $\mathcal{C}$ with $t$-structure $(\mathcal{C}_{\geq 0}, \mathcal{C}_{\leq 0})$, the prestable $\infty$-category $\mathcal{C}_{\geq 0}$ and the abelian category $\mathcal{C}^{\heartsuit}$. We prove that weak localizing subcategories of $\mathcal{C}^{\heartsuit}$ are in bijection with the localizing subcategories of $\mathcal{C}$ where object-containment can be checked on the heart. This generalizes similar known correspondences for noetherian rings and bounded $t$-structures. We also prove that this restricts to a bijection between localizing subcategories of $\mathcal{C}^{\heartsuit}$, and localizing subcategories of $\mathcal{C}$ that are kernels of $t$-exact functors -- lifting Lurie's correspondence between localizing subcategories in $\mathcal{C}_{\geq 0}$ and $\mathcal{C}^{\heartsuit}$ to the stable category $\mathcal{C}$.